
The Wigner's friend scenario, non-locality, and other quandaries should be formulated and analysed in the fact-net framework, hoping some light could be shed on them.

Our focus on facts between systems instead of the systems themselves has a clear category-theoretic inspiration. Further investigations toward a representation theory of fact nets as diagrams in the category of Hilbert spaces and partial isometries are currently carried out in the hope to close the gap with previous attempts of Yang [1]} to replace quantum states by relation matrices between states.

Our construction of the self-space of a system has only been thoroughly presented in the finite case and still has to be extended to infinite fact-sets equipped with measurable structures.

The information-theoretic flavour of the relational interpretation is not yet reflected in the fact-net formalism. However, one can already see how the structure of a fact-net allows systems to acquire varying amounts of information on one another. A formal correspondence involving von Neumann entropy still has to be figured out.

Through examples we have already seen that quantum reference frames are a promising field of application of fact-nets. Extensions of fact-nets to situations involving gauge symmetries are under development, and the links with the perspective neutral approach [2]} and the measurement-theoretic setup of [3]} are investigated. Dropping the assumption of the incompatibility of parallel facts seems a promising move towards encompassing general POVM and imperfect quantum reference frames.

Finally, the emergence of classicality and causality in fact-nets still has to be clarified, notably by a more in-depth study of the chain property.

